Dynamos with feedback of jxB force on meridional flow and differential rotation
Matthias Rempel (High Altitude Observatory
National Center for Atmospheric Research
Boulder Colorado USA)
Mausumi Dikpati (National Center for Atmospheric Research)
Keith MacGregor (National Center for Atmospheric Research)
Flux-transport dynamos have been proven to be a very successful approach
for modeling the evolution of the large scale solar magnetic field.
However, these studies addressed the transport of magnetic field by the
meridional circulation in a purely kinematic approach. The toroidal field
strength at the base of the solar convection zone inferred from studies
of rising magnetic flux tubes is around 100 KG and thus orders of magnitude
larger than the equipartition field strength estimated from a meridional
flow velocity of a few m/s. Therefore it is crucial for flux-transport
dynamos to address the feedback of the jxB on the meridional flow. In this
paper we present two approaches: 1) A kinematic approach in which we
parameterize this feedback in terms of a non-linear quenching of the
meridional flow in regions of strong field. 2) A MHD approach in which
we solve the full set of hydrodynamic equations together with the dynamo
equations. Since we focus in this approach only on the large scale flow
field, the anisotropic turbulent transport of angular momentum responsible
for the differential rotation is parameterized. From both studies we conclude
that Babcock-Leighton flux-transport dynamos work even with strong feedback of
the jxB force for mainly two reasons: 1) The transport of the weak poloidal
magnetic field is not affected strongly. 2) The meridional flow results from
a small difference between large forces, so that the transport capability is
much larger than a simple estimate based on equipartition field strengths
suggests.
This work is partially supported by NASA grants W-10107 and
W-10175. The National Center for Atmospheric Research is
sponsored by the National Science Foundation.